1. ## Integration help

$\displaystyle \int sec^45x dx$
$\displaystyle =\int (sec^25x)(sec^25x) dx$
$\displaystyle =\int (1+tan^25x)sec^25x dx$
$\displaystyle =\int (sec^25x + tan^25xsec^25x)dx$
$\displaystyle =\int sec^25x dx + \int tan^25xsec^25x dx$
$\displaystyle =\frac{1}{5}tan5x + ??????$

I don't know what to do with the second integral, or if I am even starting this problem the right way. I have the solution, but it is missing all of the steps past the trig identity. TIA.

2. ## Re: Integration help

Originally Posted by wondering
$\displaystyle \int sec^45x dx$
$\displaystyle =\int (sec^25x)(sec^25x) dx$
$\displaystyle =\int (1+tan^25x)sec^25x dx$
$\displaystyle =\int (sec^25x + tan^25xsec^25x)dx$
$\displaystyle =\int sec^25x dx + \int tan^25xsec^25x dx$
$\displaystyle =\frac{1}{5}tan5x + ??????$
$\displaystyle =\int sec^25x dx + \int tan^25xsec^25x dx$
$\displaystyle =\frac{1}{5}tan5x + \frac{1}{15}\tan^3(5x)+C$

3. ## Re: Integration help

Thanks Plato. Is it just a simple u substitution that I am not seeing? Can you explain the second integral in steps for me. Thanks for your help.

4. ## Re: Integration help

Never mind I see it now. Thanks for the help, I was having a mental block for a moment there.